Two inlet pipes M and N alone can fill a tank in 12 hours and 15 hours respectively and an outlet pipe P alone can empty the whole tank in 9 hours. First pipe M is opened for 4 hours, then pipe P is opened for 3 hours and rest of the tank is filled by pipe N. In what time will the tank be filled completely?

Solution

Total capacity = 180 units (LCM of 12, 15 and 9) Efficiency of pipe M = 180/12 = 15 units/hr Efficiency of pipe N = 180/15 = 12 units/hr Efficiency of pipe P = 180/-9 = -20 units/hr Capacity of tank filled by pipe M in 4 hours = 15 × 4 = 60 units Capacity of tank emptied by pipe P in 3 hours = -20 × 3 = -60 units Capacity of tank left for pipe N = 180 – 60 – (-60) = 180 units Time taken by pipe N to fill the remaining tank = 180/12 = 15 hrs Total time taken = 4 + 3 + 15 = 22 hrs